みどり in this sentence is not an adjective ("green", "greenish"), but a noun meaning "greenery".

きれい is an adjective modifying the above noun.

The whole sentence reads then as "It is a town with beautiful greenery".

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が in effect does not connect two adjectives, but a part of relative clause. Either みどりのきれい or みどりがきれい can be used here, see [this question](https://japanese.stackexchange.com/q/12825/11104).